Domain decomposition methods for the Eikonal equation.
A. Chacon (CAM, Cornell)
The Eikonal equation is a 1st order nonlinear static PDE that is used to model wavefront propagation and optimal control problems. The equation is also related to shortest path problems on graphs. Recently several fast algorithms for solving the equation have been developed. Two of the most popular methods, the Fast Sweeping Method and the Fast Marching Method, perform well on a different set of Eikonal equations. I will discuss each method's strengths and weaknesses, then present a family of new fast two-scale hybrid methods based on the ideas of Fast Marching and Fast Sweeping. This is joint work with Alex Vladimirsky